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NUMERACY AND THE MATHEMATICS CURRICULUM:

Numeracy Professional Development Projects Supplement 2006

Numeracy arises out of effective mathematics teaching.All the strands within Mathematics in the New ZealandCurriculum are important in the pathway to numeracy.Number is central to this pathway, although the relativeemphasis on this strand changes with the stages ofschooling:� in the first four years of schooling, the main

emphasis should be on the number strand;� in the middle and upper primary years of

schooling, the emphasis is spread across thestrands of the curriculum;

� towards the end of compulsory schooling, numbersense becomes a tool for use across the otherstrands.

At all stages, students should:� develop an understanding of numbers, the ways

they are represented, and the quantities for whichthey stand;

� develop accuracy, efficiency, and confidence incalculating � mentally, on paper, and with acalculator;

� develop the ability to estimate and to makeapproximations, and to be alert to thereasonableness of results and measurements.

(Mathematics in the New Zealand Curriculum, page 31)

These achievement aims enable students to develop theability and inclination to use mathematics to solveproblems in a range of contexts.

Published by the Ministry of Education.PO Box 1666, Wellington, New Zealand.

Copyright © Crown 2006. All rights reserved.Enquiries should be made to the publisher.

ISBN 0 478 13216 6Dewey number 372.7Topic Dewey number 510

Item number 13216

Note: Teachers may copy these notes for educational

purposes.

This book is also available on the New Zealand Maths website,

at www.nzmaths.co.nz/Numeracy/2006numPDFs/pdfs.htm

The general aims of mathematics education in NewZealand define the features of school programmes thatcontribute to the development of numerate people.Such programmes:� help students to develop a belief in the value of

mathematics and its usefulness to them, tonurture confidence in their own mathematicalability, to foster a sense of personal achievement,and to encourage a continuing and creativeinterest in mathematics;

� develop in students the skills, concepts,understandings, and attitudes which will enablethem to cope confidently with everyday life;

� help students to develop a variety of approachesto solving problems involving mathematics, and todevelop the ability to think and reason logically;

� help students to achieve the mathematical andstatistical literacy needed in a society which istechnologically oriented and information rich;

� provide students with the mathematical tools,skills, understandings, and attitudes they willrequire in the world of work;

� provide a foundation for those students who maycontinue studies in mathematics or other learningareas where mathematical concepts are central;

� help to foster and develop mathematical talent.(Mathematics in the New Zealand Curriculum, page 8)

Although the groundwork is laid in mathematics, othercurriculum areas also provide opportunities fornumeracy learning. In addition, the home, earlychildhood settings, and the community assist in thedevelopment of numeracy.

Enriching the Number Framework with Beginning School Mathematics

IntroductionThis booklet is a practical guide to help teachers to effectively use Beginning School Mathematics (BSM) in the deliveryof Mathematics in the New Zealand Curriculum in their classrooms. Key BSM activities have been selected to supportthe teaching and learning of the knowledge and strategies in the Number Framework.

The Numeracy Project and the Beginning School Mathematics resource share these beliefs about mathematics learning:� Children experience mathematical ideas and develop mathematical skills and understanding before they start school.� Children learn by relating new ideas to their existing experience and ideas.� Children learn best when ideas are presented in realistic and meaningful contexts.� Using equipment is a powerful way of developing children�s mathematical understanding.� Effective mathematics teaching involves a range of approaches.� Children learn in different ways and at different rates.� Concepts can be presented in a variety of ways to match different learning styles.� Learning involves taking risks in a supportive environment.� The needs of the learner must be at the heart of all planning.� Feedback can take many forms and is an essential part of the learning process.� Critical reflection and effective communication of ideas are essential learning tools.

Effective use of BSM by teachers will also support the delivery of the process strands of Mathematics in the New ZealandCurriculum. Teacher-child interaction will elicit language (Communicating Mathematical Ideas), develop discussionabout strategies (Problem Solving), and encourage flexible thinking (Logic and Reasoning).

The BSM resource does positively influence children�s mathematics learning and their attitudes towardsmathematics. The views expressed by teachers, principals, parents and caregivers, together with the reported(and observed) enthusiasm shown by children when they were using the BSM resource, all provide convincingevidence that BSM is a very good resource for the teaching and learning of mathematics in the junior school.

An Evaluation of the Resource Beginning School Mathematics, Ministry of Education, 1996

The possibilities and potential of BSM are as flexible as the teacher, who continues tohold the key to its effective use.

1

Enriching the Number Framework with Beginning School Mathematics

2

The Relationships between the Ministry of Education’s MathematicsPolicy Statements and Resources

National Education Guidelines

The New Zealand Curriculum Framework

Ministry of Education resources� Beginning School Mathematics (BSM)

� Figure It Out

� nzmaths website

� Connected

� Numeracy Development Project Support Material

Mathematics in the New Zealand Curriculum

Non-number strands The Number Framework

Enriching the Number Framework with Beginning School Mathematics

Knowing the Beginning School Mathematics ResourceBSM is designed to be used by children in their first three years of schooling. The resource is made up of twelve cycles,and these support all strands of Mathematics in the New Zealand Curriculum.

Each cycle is divided into three modules, and each module contains numbered activities. For example, cycle 9, module3, activity 51 is numbered 9-3-51. The numbering system is consistent throughout the resource and allows the componentsto be easily identified for borrowing or reshelving.

The Structure of Beginning School Mathematics

Cycle 7

Module 2

Space, Relationships,Measurement

Cycle 7

Module 1

Number, Relationships,Operations

Cycle 7

Module 3

More Attributes, Patterns,Operations

BSM Cycle 7

Assessment� Numeracy Project Assessment (NumPA)

� Assessment Resource Banks (ARBs)

� National Education Monitoring Project (NEMP)

� Assessment Tools for Teaching and Learning (AsTTle)

� National Mathematical Exemplars

3

Enriching the Number Framework with Beginning School Mathematics

The Components of Beginning School Mathematics

Overview charts: There are two overview charts, one covering cycles 1 to 6 and the other cycles 7 to 12. The chartsoutline the content of each cycle and show how ideas are introduced and developed. The charts reflect the progressionsoutlined in the knowledge and strategy frameworks.

Teachers� guides and copymasters: The teachers� guides contain the aims and objectives, information on mathematicalideas, and suggested developments for learning activities. The copymasters contain material for teachers to use whenpreparing for teaching. They also contain recording sheets for children.

Children�s booklets, direction cards, and recording sheets: These components can be used for children to work withindependently. They are used with cycles 7 to 12.

Checkpoints: There are checkpoints for each cycle. Teachers may find that these contain some useful ideas for checkingaspects of children�s learning.

Card equipment and hardware: Card equipment is supplied to match particular activities in the resource. It is numberedto match the activity (see page 4). Cardware is available from Learning Media Customer Services.

The BSM hardware and other standard mathematical equipment required for BSM activities are described in the teachers�guides. These materials can be obtained from suppliers of educational equipment.

Suggested Hardware Materials to Support BSM Activities

Children�s booklets,direction cards, and

recording sheets

Card equipmentand hardware

Overview charts

Teachers� guidesand copymasters Checkpoints

Refer to Beginning School Mathematics: A Guide to the Resource, Learning Media, 1994, for further information aboutthe resource. This book was distributed to schools in 1994. If it is no longer in your school, you can download it fromthe nzmaths website.

StorageSchools need to ensure that their BSM resource is stored so that teachers can access it easily. It is suggested that schoolsretain the original organisation of the resource in cycles and modules. Within the classroom, mathematical equipmentshould also be accessible and easy to retrieve.

Beads and threadersInterlocking cubesMosaic pattern shapesCuisenaire rodsCountersPegboards and pegsShape/animal/vehicle attribute setsPattern boards and blocksNursery sticks

CalculatorsClocksEgg-timersGeoboards and rubber bandsAttribute logic blocksHundreds boardsCollections of buttons, bottle tops, shells, stones, acorns, etc.Sorting boxes of odds and ends.

With its rich bank of manipulative materials and activities, BSM is an excellent supporting resource forthe numeracy project. Knowledge consolidation is supported through teacher-led activities, many ofwhich can then be used independently. Teachers can select, alter, or adapt activities to meet the changinglearning needs of their students.

4

Linking Beginning School Mathematics to the Number FrameworkThe tables on pages 6�16 show how BSM activities can be used to support the Number Framework. The tables arearranged according to the five content domains of the knowledge section of the Framework and the three operationaldomains of the strategies section. The content domains are number identification, number sequence and order,grouping/place value, basic facts, and written recording, and the operational domains are addition/subtraction,multiplication/division, and proportions and ratios.

The BSM activities are identified as being suitable for teacher-led activities (T), class activities (C), and independentactivities (I). Many teacher-led learning experiences can become independent activities.

For example:

Advanced Counting Stage 4

Basic Facts Addition andSubtraction

BSM activity

9-1-4

9-1-42

9-1-6

NumeralIdentification

T

T I

T

NumberSequence/Order

T

I

Grouping andPlace Value

T

I

T

WrittenRecording

Multiplicationand Division

Proportionsand Ratios

Knowledge Strategies

T � Teacher-led activity C � Class activity I � Independent activity

The BSM teachers� guides explain how to develop the lesson content to achieve the learning outcomes. Each guidealso contains information to reinforce teachers� mathematical content knowledge and pedagogy.

Cycle 1 activities have not been related to the stages of the Number Framework. These learning experiences can beused to help children at the Pre-emergent stage to gain early mathematical understandings. For children at the Emergentstage, the cycle 1 activities will develop language and provide the foundation for further mathematical learning.

Beginning at Stage 2, children need to be taken from the use of materials to imaging (the visualisation of materials).This is not clearly stated in the BSM resource. While no specific activities have been identified for children workingat the Counting from One by Imaging stage, teachers can use those activities from the previous stage (Counting fromOne on Materials) to continue to create strong visual images. They can shield the materials from the children andencourage them to image these materials in order to solve the problem. An empty template has been provided forteachers to record their own selection of activities suitable for use at the Counting from One by Imaging stage.

As Number underpins all mathematical learning, the BSM activities relating to the other strands (Measurement,Geometry, Algebra, and Statistics) are listed according to the stages of the Number Framework. (See the tables onpages 17�23.) This will enable these to be taught concurrently with Number. There is a wealth of learning experiencesrelating to logic and reasoning in the BSM resource, and these have been listed under each stage. The problem-solvingand communication processes are implicit in all activities but will need to be made explicit by the teacher.

Enriching the Number Framework with Beginning School Mathematics

T T

The Use of QuestioningThe importance of questioning children about their thinking, giving them time to respond, and giving specific feedbackon their responses cannot be overemphasised. Both open and closed questions can be used when working with children.

Teachers are encouraged to share the questions below with:� parents and caregivers in newsletters and at parents� nights� children so they can ask each other the questions.

These suggested questions will help to develop children�s mathematical thinking and learning:� Can you tell me how you did that?� Can you explain what you were thinking as you did that?� Can you do that another way?� Could you estimate how many you think it will be?� How many other ways could you do that?� How did you do that?� Is there something you already know that will help you to do this?� Is that what you thought would happen?� What did you think of as you worked that out?� What could we find out?� What do you want to find out?� What do you think might happen here?� What can you tell me about what you have done?� Tell me how you worked that out.

Teachers can photocopy this page and use it for teaching purposes, school newsletters, and family maths evenings andput it on the wall for children to look at.

Schools’ Entitlement to BSM Books and Card EquipmentTeachers� GuidesOne copy per teacher of junior classes

Students� BooksOne copy for every nine students in junior classes

Card EquipmentOne set for every 40 students in junior classes, up to a maximum of four sets

Notes:

� Lost or damaged items will be replaced free on request. Only individual items of card equipment will bereplaced, not whole sets. We suggest that schools do a stocktake of BSM items each year in October so thatorders for replacement can be placed in November with the aim of having a full inventory for the start ofterm 1 the following year.

� Although teachers� guides are supplied on the basis of one copy per junior class teacher, the books are the propertyof the school. Teachers moving to another school should expect to find copies available when they arrive.

Schools can obtain these books and equipment from Learning Media Customer Services:freefax: 0800 800 570email: [email protected]: 0800 800 565

5

Enriching the Number Framework with Beginning School Mathematics

6

BSM activity

2-1-1

2-1-2

2-1-21

2-1-22

2-1-81

2-1-4

2-1-82

2-1-84

2-3-7

2-3-24

2-3-8

2-3-13

2-3-55

2-3-81

3-1-2

3-1-21

3-1-22

3-1-3

3-1-49

3-1-4

3-1-5

3-1-6

3-1-7

3-1-23

3-1-45

3-1-46

3-1-47

3-1-81

3-1-82

3-3-9

3-3-22

3-3-48

3-3-49

3-3-81

BSM Activities Suitable for Each Stage of the Number FrameworkEmergent Stage 0

Addition andSubtraction

T

NumeralIdentification

T

T

T

T I

I

T I

C

C

T I

T

T

T

C

I

I

I

I

I

I

NumberSequence/Order

C

C

C

C

T

C

C

C

T

T

T

C

I

I

C

I

I

I

Grouping andPlace Value

T

T

C

C

I

T

I

T I

T

I

T I

I

T

I

T I

T

T

T

C

I

I

I

I

I

T

WrittenRecording

I

C

Multiplicationand Division

T

C

Knowledge Strategies

Proportionsand Ratios

T

C

Basic Facts

Enriching the Number Framework with Beginning School Mathematics

7

One-to-one Counting Stage 1

BSM activity

2-1-5

3-1-43

4-1-22

4-1-23

4-1-44

4-1-45

4-1-47

4-1-48

4-1-83

4-1-5

4-1-50

4-1-82

4-3-5

4-3-6

4-3-21

4-3-44

4-3-84

4-3-46

4-3-24

4-3-25

4-3-51

5-1-3

5-1-6

5-1-46

5-1-7

5-1-8

5-1-21

5-1-22

5-1-83

5-3-5

5-3-22

5-3-45

5-3-46

5-3-82

5-3-6

5-3-48

5-3-7

5-3-23

5-3-49

5-3-83

Addition andSubtraction

T

C

C

T

T

T

NumeralIdentification

C

C

I

I

I

T

I

T

T I

T I

T

C

T

T I

T I

C

C

T

T

I

T

T

C

C

I

T

I

T I

T I

I

NumberSequence/Order

T

I

C

I

I

I

I

T

T I

T I

T

T

T I

I

C

C

T I

T

T

T

C

C

C

I

T

C

I

T I

T I

I

T I

C

Grouping andPlace Value

T

C

I

I

I

I

T

T I

T I

T

T

C

T

T I

T I

T

T

I

T

C

I

T

C

I

T I

T I

T I

C

I

T

WrittenRecording

C

T I

Multiplicationand Division

Knowledge Strategies

Proportionsand Ratios

Basic Facts

Enriching the Number Framework with Beginning School Mathematics

8

BSM activity

6-1-3

6-1-21

6-1-4

6-1-43

6-1-5

6-1-6

6-1-44

6-1-7

6-1-45

6-1-46

6-1-81

6-1-82

6-1-9

6-2-21

6-2-22

6-2-9

6-2-48

6-3-3

7-1-1

7-1-41

7-1-42

7-1-81

7-1-2

7-1-43

7-1-3

7-1-44

7-1-46

7-2-7

7-2-48

7-2-49

7-2-82

7-3-4

8-2-8

8-2-47

8-2-48

8-2-83

9-2-18

9-2-61

9-2-85

Addition andSubtraction,Place Value

C

T

T

T

T

T

NumeralIdentification

T

T

T

T

T

I

T

T

T

C

C

T

T

I

T I

T I

T

NumberSequence/Order

T

T

T

T

I

T

T

T

T I

T I

T

T

Grouping andPlace Value

T

C

T

T I

T

T

T I

T I

T I

T

T

T

I

T

WrittenRecording

I

I

I

I

T I

T I

T I

T I

Multiplicationand Division

Knowledge Strategies

Proportionsand Ratios

T

T

I

T

T I

I

I

T I

T

I

I

T

T I

T I

Basic Facts

I

I

I

One-to-one Counting Stage 1 (continued)

Enriching the Number Framework with Beginning School Mathematics

9

BSM activity

6-1-3

6-1-4

6-1-5

6-1-6

6-1-21

6-1-7

6-1-43

6-1-44

6-1-45

6-1-46

6-1-81

6-1-82

6-1-9

6-1-47

6-2-9

6-2-48

6-3-21

6-3-22

6-3-3

6-3-81

6-3-82

6-3-4

6-3-5

6-3-6

6-3-7

6-3-8

6-3-49

7-1-1

7-1-41

7-1-42

7-1-81

7-1-2

7-1-43

7-1-46

7-1-82

7-1-48

7-1-49

7-1-50

7-1-6

7-1-52

Addition andSubtraction

T

C

T

T

T

T

T

T

T I

T

T

T I

T

T I

T I

T

T I

NumeralIdentification

T

T

T

T

T

I

T

T

C

C

T I

T I

T I

T

T I

I

T I

T I

I

I

NumberSequence/Order

T

T

T

T

T

I

T I

T

T I

T I

T I

T I

T I

I

I

Grouping andPlace Value

T

T

C

T

T I

T I

T I

T I

T

T

T I

I

T

T I

T

I

WrittenRecording

T

T

I

I

T

I

Counting from One on Materials Stage 2

Multiplicationand Division

Knowledge Strategies

Proportionsand Ratios

T

T

Basic Facts

I

I

I

Enriching the Number Framework with Beginning School Mathematics

10

Enriching the Number Framework with Beginning School Mathematics

Multiplicationand Division

T

T

T I

Basic Facts

Counting from One on Materials Stage 2 (continued)

BSM activity

7-1-53

7-1-85

7-3-4

7-3-7

7-3-82

8-1-4

8-1-45

8-1-5

8-1-46

8-1-47

8-1-82

8-1-49

8-1-8

8-1-50

8-1-51

8-1-52

8-1-83

8-1-84

8-1-10

8-1-53

8-1-85

8-3-6

8-3-47

8-3-48

8-3-49

8-3-82

8-3-50

8-3-51

8-3-9

Addition andSubtraction

T I

T I

T

T

T I

T

T

T

T

T

T

T

T I

T

T

T

T

NumeralIdentification

T

T

NumberSequence/Order

T

T

T

Grouping andPlace Value

T

T

T

T

WrittenRecording

I

T I

T

T I

T I

I

I

I

T I

I

T I

T I

I

I

T I

I

I

I

T I

Knowledge Strategies

Proportionsand Ratios

T I

T I

I

I

I

11

Counting from One by Imaging Stage 3

BSM activity Addition andSubtraction

NumeralIdentification

NumberSequence/Order

Grouping andPlace Value

WrittenRecording

Multiplicationand Division

Knowledge Strategies

Proportionsand Ratios

Basic Facts

Enriching the Number Framework with Beginning School Mathematics

This empty template has been provided for teachers to record their own selection of activities suitable for use at theCounting from One by Imaging Stage. (See page 4.)

12

Advanced Counting Stage 4

BSM activity

9-1-4

9-1-42

9-1-6

9-1-8

9-1-45

9-1-46

9-1-83

9-1-84

9-1-9

9-1-10

9-1-47

9-1-48

9-1-12

9-1-13

9-1-51

9-1-52

9-1-53

9-1-54

9-1-85

9-1-86

9-1-14

9-1-15

9-1-16

9-2-18

9-2-61

9-2-85

9-3-48

9-3-84

9-3-9

9-3-51

9-3-52

9-3-10

9-3-53

9-3-11

9-3-12

9-3-13

9-3-55

9-3-14

9-3-58

9-3-85

Addition andSubtraction

T

T

T

T

I

I

T

I

I

T

T

T I

T I

T

T

T

T

T I

T

T

T

NumeralIdentification

T

T I

T

T

T

NumberSequence/Order

T

I

T I

I

I

WrittenRecording

T

T

T I

T I

I

I

T

T

I

T I

T I

T I

I

T

T

I

T I

T I

T

T

I

I

Multiplicationand Division

T

T

T

T

T I

T

T I

T I

Knowledge Strategies

Proportionsand Ratios

T I

I

I

T

T I

Basic Facts

T

T

T

T I

I

I

T

I

I

Grouping andPlace Value

T

I

T

T

T

T I

T

T

T

T

T

T

Enriching the Number Framework with Beginning School Mathematics

13

BSM activity

10-1-2

10-1-41

10-1-3

10-1-42

10-1-82

10-1-4

10-1-6

10-1-47

10-1-48

10-1-7

10-1-49

10-3-84

10-3-6

10-3-46

10-3-8

10-3-53

10-3-9

10-3-56

10-3-86

10-3-11

11-1-3

11-1-6

11-1-47

11-1-48

11-1-7

11-1-49

11-1-50

11-1-52

11-1-83

11-1-84

11-2-18

11-2-59

11-3-4

11-3-44

11-3-8

11-3-9

11-3-50

11-3-10

11-3-12

11-3-13

Addition andSubtraction

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

T

NumeralIdentification

T

T

T

T

T

T

T

T

T

T

NumberSequence/Order

T

C

T

WrittenRecording

I

T I

I

I

I

T

I

T

I

I

T

I

I

I

I

I

I

I

I

T

I

I

T

T

Multiplicationand Division

C

T

T

T

Knowledge Strategies

Proportionsand Ratios

T

T

Basic Facts

T

I

I

T

T

T I

I

I

I

T

T

I

Grouping andPlace Value

T

T

T

C

T

T

T

T

T

I

I

T

T

I

Advanced Counting Stage 4 (continued)

Enriching the Number Framework with Beginning School Mathematics

14

Basic Facts Multiplicationand Division

T

T

T

Proportionsand Ratios

Advanced Counting Stage 4 (continued)

BSM activity

11-3-54

11-3-55

12-1-1

12-1-5

12-1-44

12-1-45

12-1-84

Addition andSubtraction

T

T

NumeralIdentification

T

T

T

T

T

NumberSequence/Order

T

T

WrittenRecording

I

I

T I

I

I

I

Knowledge Strategies

Grouping andPlace Value

T

Enriching the Number Framework with Beginning School Mathematics

15

Early Additive Part-Whole Stage 5

BSM activity

11-3-12

11-3-13

11-3-54

11-3-55

12-1-3

12-1-4

12-1-42

12-1-43

12-1-6

12-1-46

12-1-7

12-1-47

12-1-48

12-1-49

12-1-50

12-1-52

12-1-9

12-1-15

12-1-55

12-1-56

Addition andSubtraction

T

T

I

I

T

I

T

T I

I

I

T I

I

T

T I

T

T

NumeralIdentification

T

T

T

I

I

I

I

NumberSequence/Order

T

T

I

I

WrittenRecording

T

T

T

Multiplicationand Division

T

Knowledge Strategies

Proportionsand Ratios

Basic Facts

T

T I

I

I

I

T

I

T

Grouping andPlace Value

T

T

I

I

T

T

I

I

T

I

I

Enriching the Number Framework with Beginning School Mathematics

16

Enriching the Number Framework with Beginning School Mathematics

BSM activity

12-1-85

12-1-86

12-1-87

12-1-89

12-3-2

12-3-45

12-3-46

12-3-47

12-3-81

12-3-82

12-3-6

12-3-7

12-3-49

12-3-50

12-3-51

12-3-83

12-3-84

12-3-8

12-3-52

12-3-53

12-3-85

12-3-13

Addition andSubtraction

I

T

I

I

T

I

I

I

I

T

I

I

I

T

NumeralIdentification

T

T

T

T

T

I

C

T

I

I

I

I

I

T

I

NumberSequence/Order

WrittenRecording

T

I

I

I

I

I

I

I

Multiplicationand Division

T

Knowledge Strategies

Proportionsand Ratios

T

I

I

I

I

I

Basic Facts

I

T

I

I

T

I

I

I

I

T

I

I

I

T

Grouping andPlace Value

Early Additive Part-Whole Stage 5 (continued)

17

Enriching the Number Framework with Beginning School Mathematics

BSM Activities That Link with the Non-number Strands of

Algebra

Exploring patterns andrelationships

2-3-11

2-3-12

2-3-25

2-3-26

2-3-27

3-1-1

3-1-41

3-3-10

3-3-23

3-3-50

3-3-51

Geometry

Exploring shape and space

Statistics

Statistical investigations

Emergent Stage 0

Measurement

Estimating and measuring

2-1-6

2-1-7

2-1-8

2-1-9

2-1-24

2-1-25

2-1-27

2-1-43

2-1-44

2-1-85

2-1-86

2-1-10

2-1-45

2-1-12

2-1-13

2-1-47

2-3-23

3-1-10

3-1-24

3-1-11

3-2-5

3-2-6

3-2-25

4-1-7

4-1-8

4-1-25

4-1-26

4-1-51

4-1-9

4-1-81

2-2-1

2-2-2

2-2-3

2-2-4

2-2-21

2-2-22

2-2-41

2-2-43

2-2-44

2-2-83

2-2-23

2-2-46

2-2-5

2-2-6

2-2-47

2-2-24

2-2-25

2-2-8

2-2-9

2-2-26

2-2-49

2-2-85

2-2-82

3-2-1

3-2-2

3-2-4

3-2-21

3-2-22

3-2-23

3-2-7

3-2-24

Exploring equations andexpressions

Exploring symmetry andtransformations

Interpreting statistical reportsDeveloping concepts of time,rate, and change

Seriation

2-1-11

2-1-46

2-3-6

2-3-50

2-3-51

3-1-8

3-1-9

3-3-7

Logic and Reasoning

Interpret information and results in context

2-3-22, 2-3-41, 2-3-4, 2-3-42, 2-3-43, 2-3-44, 2-3-45, 2-3-84, 2-3-85, 2-3-5, 3-3-21, 3-3-41, 3-3-3, 3-3-4, 3-3-44

Classify objects

2-3-1, 2-3-22, 2-3-41, 2-3-2, 2-3-3, 2-3-4, 2-3-21, 2-3-42, 2-3-43, 2-3-44, 2-3-45, 2-3-84, 2-3-85, 2-3-5, 3-3-1, 3-3-42, 3-3-2,3-3-3, 3-3-43, 3-3-4

18

Enriching the Number Framework with Beginning School Mathematics

Seriation

4-1-7

5-3-4

5-3-44

Algebra

Exploring patterns andrelationships

4-1-1

4-1-21

4-1-41

4-3-11

4-3-12

4-3-83

5-1-1

5-1-51

5-3-9

5-3-11

5-3-56

5-3-86

5-3-6

5-3-48

Geometry

Exploring shape and space

Statistics

Statistical investigations

One-to-one Counting Stage 1

Measurement

Estimating and measuring

4-2-4

4-2-45

4-2-5

4-2-46

4-2-82

4-2-22

4-2-23

5-1-48

5-1-11

5-1-49

5-1-50

5-2-5

5-2-43

5-2-81

5-2-4

5-2-21

5-2-22

5-2-44

5-2-6

5-2-7

5-2-45

3-2-41

3-2-42

3-2-43

3-2-44

3-2-46

3-2-81

3-2-45

3-2-47

4-2-1

4-2-21

4-2-41

4-2-81

4-2-2

4-2-42

4-2-3

4-2-43

4-2-44

4-2-47

4-2-25

5-2-1

5-2-41

5-2-42

5-2-2

5-2-3

5-2-24

5-2-25

5-2-50

5-2-51

5-2-52

6-2-1

6-2-2

6-2-82

6-2-41

6-2-3

6-2-21

6-2-42

6-2-81

6-2-83

7-2-1

7-2-41

7-2-42

8-2-49

8-2-50

Exploring equations andexpressions

Exploring symmetry andtransformations

Interpreting statistical reportsDeveloping concepts of time,rate, and change

4-2-6

4-2-7

5-2-9

5-2-10

5-2-23

5-2-48

5-2-11

5-2-49

2-3-9

2-3-10

2-3-27

2-3-53

2-3-86

2-3-87

3-3-8

3-3-85

5-3-10

7-2-2

7-2-43

7-2-44

7-2-81

7-2-82

7-3-5

7-3-47

7-3-48

Classify objects

4-3-82, 4-3-2, 4-3-3, 4-3-41, 4-3-42, 4-3-43, 4-3-86, 4-3-4, 5-3-1, 5-3-41, 5-3-42, 5-3-2, 5-3-43, 5-3-81, 5-3-3

Logic and Reasoning

Interpret information and results in context

4-3-1, 4-3-2, 4-3-3, 4-3-42, 4-3-43, 5-3-1, 5-3-41, 5-3-42, 5-3-2, 5-3-43, 5-3-81, 5-3-3, 5-3-21

4-1-1

4-1-26

4-1-41

4-1-2

4-1-21

5-1-2

5-1-84

19

Enriching the Number Framework with Beginning School Mathematics

Algebra

Exploring patterns andrelationships

Geometry

Exploring shape and space

Statistics

Counting from One on Materials Stage 2

Measurement

Estimating and measuring

6-1-10

6-2-4

6-2-43

6-2-5

6-2-24

7-2-3

7-2-45

7-2-46

7-2-4

7-2-5

7-2-47

8-2-1

8-2-41

8-2-42

8-2-81

8-2-2

8-2-3

8-2-43

8-2-4

8-2-5

8-2-44

8-2-45

8-2-46

6-1-1

6-1-4

6-1-6

6-1-44

6-3-1

6-3-3

6-3-47

6-3-48

7-1-42

7-1-44

7-1-82

7-1-4

7-1-54

7-3-3

7-3-4

7-3-6

7-3-49

7-3-81

8-1-1

8-1-41

8-1-3

8-1-43

8-1-44

8-1-48

8-3-5

8-3-10

Logic and Reasoning

Interpret information and results in context

6-3-1, 6-3-41, 6-3-42, 6-3-51, 7-3-2, 7-3-43

Classify objects

6-3-1, 6-3-41, 6-3-42, 6-3-51, 7-3-1, 7-3-41, 7-3-42, 7-3-2, 7-3-43

Exploring equations andexpressions

7-3-3

7-3-44

7-3-7

8-1-3

8-1-44

8-3-3

8-3-44

8-3-45

8-3-4

8-3-46

Exploring symmetry andtransformations

Interpreting statistical reportsDeveloping concepts of time,rate, and change

6-2-7

6-2-47

6-2-8

6-2-23

7-2-51

8-2-7

8-2-46

8-2-82

Money

5-2-8

6-2-6

6-2-22

6-2-45

6-2-46

7-2-6

7-2-50

Statistical investigations

6-1-1

6-1-41

6-1-2

Statistical investigations

7-1-54

8-1-1

8-1-41

8-1-2

8-1-42

20

Enriching the Number Framework with Beginning School Mathematics

Counting from One by Imaging Stage 3

Algebra

Exploring patterns andrelationships

Geometry

Exploring shape and space

StatisticsMeasurement

Estimating and measuring

6-1-1

6-1-4

6-1-6

6-1-44

6-3-1

6-3-3

6-3-47

6-3-48

7-1-42

7-1-44

7-1-82

7-1-4

7-1-54

7-3-3

7-3-4

7-3-6

7-3-49

7-3-81

8-1-1

8-1-41

8-1-3

8-1-43

8-1-44

8-1-48

8-3-5

8-3-10

Classify objects

8-3-1, 8-3-41, 8-3-81 ,8-3-2, 8-3-42, 8-3-43

Logic and Reasoning

Interpret information and results in context

8-3-2, 8-3-42, 8-3-43

Exploring equations andexpressions

Exploring symmetry andtransformations

Interpreting statistical reportsDeveloping concepts of time,rate, and change

7-3-3

7-3-44

7-3-7

8-1-3

8-1-44

8-3-3

8-3-44

8-3-45

8-3-4

8-3-46

21

Enriching the Number Framework with Beginning School Mathematics

Advanced Counting Stage 4

Classify objects

9-3-1, 9-3-2, 9-3-3, 9-3-41, 9-3-42, 9-3-43, 9-3-81, 9-3-82, 9-3-4, 9-3-44, 10-3-1, 10-3-2, 10-3-3, 10-3-41, 10-3-4, 10-3-5,10-3-42, 10-3-43, 10-3-44, 10-3-45, 10-3-15, 10-3-61, 10-3-62

11-2-12

11-2-48

11-2-49

11-2-50

11-2-51

11-2-83

11-2-13

11-2-14

11-2-52

11-2-54

11-2-53

12-2-6

12-2-7

12-2-48

12-2-49

12-2-10

Algebra

Exploring patterns andrelationships

Geometry

Exploring shape and space

Logic and Reasoning

Interpret information and results in context

11-3-1, 11-3-2, 11-3-41

Measurement

Estimating and measuring

9-2-48

9-3-82

9-3-5

10-1-6

10-1-47

10-1-48

10-1-83

10-3-11

10-3-57

10-3-58

11-3-4

11-3-5

11-3-43

11-3-44

11-3-45

11-3-81

11-3-82

11-3-14

11-3-15

12-1-1

12-1-2

12-1-41

12-1-81

9-2-1

9-2-41

9-2-42

9-2-43

9-2-44

9-2-81

9-2-6

9-2-7

9-2-46

9-2-49

10-2-1

10-2-41

10-2-42

10-2-81

10-2-2

10-2-43

10-2-82

10-2-83

10-2-3

10-2-4

10-2-5

10-2-44

10-2-6

10-2-7

10-2-8

10-2-45

10-2-46

11-2-1

11-2-2

11-2-41

11-2-3

11-2-42

11-2-43

11-2-4

11-2-5

11-2-44

11-2-6

11-2-7

11-2-46

11-2-8

11-2-9

11-2-47

11-2-82

Statistics

Statistical investigations

9-1-1

9-1-2

9-1-3

9-1-41

9-1-81

10-1-1

11-1-1

22

Enriching the Number Framework with Beginning School Mathematics

9-2-16

9-2-56

9-2-57

9-2-58

10-2-13

10-2-14

10-2-15

10-2-51

10-2-52

11-2-9

11-2-82

11-2-10

11-2-16

11-2-17

11-2-57

11-2-58

11-2-84

Algebra

Exploring equations andexpressions

Geometry

Exploring symmetry andtransformations

Advanced Counting Stage 4 (continued)

Measurement

Developing concepts of time,rate, and change

9-1-11

9-1-49

9-3-5

9-3-45

9-3-46

9-3-47

10-3-7

10-3-48

10-3-49

10-3-50

10-3-51

10-3-85

11-1-4

11-1-5

11-1-43

11-1-44

11-1-45

11-1-46

11-3-6

11-3-7

11-3-46

11-3-48

11-3-83

9-2-82

9-2-2

9-2-4

9-2-5

9-2-45

10-2-4

10-2-7

10-2-8

10-2-45

10-3-12

10-3-13

10-3-14

10-3-59

10-3-60

11-2-1

11-2-2

11-2-41

11-2-81

9-1-1

9-1-2

9-1-3

9-1-41

9-1-81

10-1-1

11-1-1

Money

9-2-17

9-2-59

9-2-60

9-2-84

11-2-45

11-2-15

11-2-55

11-2-56

12-2-14

12-2-54

12-2-55

Money activities includedin Number

12-2-43

12-2-13

12-2-14

12-2-54

12-2-55

Statistics

Interpreting statistical reports

Statistical investigations

Money

23

Enriching the Number Framework with Beginning School Mathematics

Algebra

Exploring patterns andrelationships

Geometry

Exploring shape and space

Statistics

Early Additive Part-Whole Stage 5

Measurement

Estimating and measuring

12-3-3

12-3-4

12-3-81

12-3-82

12-2-1

12-2-2

12-2-42

12-2-43

12-2-3

12-2-4

12-2-44

12-2-45

12-2-46

12-2-47

12-2-16

Logic and Reasoning

Interpret information and results in context

12-3-1, 12-3-41, 12-3-42, 12-3-43, 12-3-44

Exploring equations andexpressions

Exploring symmetry andtransformations

Interpreting statistical reportsDeveloping concepts of time,rate, and change

12-3-3

12-3-4

12-3-81

12-3-82

12-2-8

12-2-9

12-2-50

12-2-51

12-2-81

12-3-12

12-3-59

12-3-60

12-3-89

12-3-90

12-3-91

Money activities includedin Number

12-3-12

12-3-59

12-3-60

12-3-89

12-3-90

12-3-91

Enriching the Number Framework with Beginning School Mathematics

BSM Activities Recommended for Deletion

5-1-9

5-1-10

5-1-45

5-1-51

5-2-46

5-2-47

5-3-24

5-3-53 (adapt � doit with number diceinstead 1�3)

5-3-54

5-3-85

Cycle 1 Cycle 6

6-1-8

6-1-42

6-1-48

6-2-44

6-2-49

6-3-43

6-3-83Cycle 2

2-1-3

2-1-26

2-1-41

2-1-83

2-2-7

2-2-42

2-2-45

2-2-81

2-2-86

2-3-54

2-3-83

Cycle 3

3-1-42

3-1-48

3-1-50

3-1-51

3-1-53

3-1-54

3-1-83

3-3-46

3-3-52

3-3-53

3-3-82

3-3-83

3-3-84

Cycle 4

4-1-52

4-1-3

4-2-83 4-3-7

4-3-23

4-3-47

4-3-49

4-3-81

4-3-85

Cycle 5

Cycle 7

7-1-47

7-1-84

Cycle 8

8-3-52

Cycle 9

9-3-8

9-3-49

9-3-50

Cycle 10

10-1-5

10-1-50

10-3-10

Cycle 11

11-1-8

11-1-9

11-1-12

11-3-11

If there is no reference to a learning activity ineither the deletions or the framework references,the activity can still be used but needs to be adaptedin some way or requires more appropriate materialsthan those being demonstrated.

Most references to learning with place value blocksin cycles 9, 10, 11, and 12 have been excluded ordeleted because children need to be introduced toplace value ideas with discrete materials first, forexample, bundles of nursery sticks or beans, beforebeing introduced to place value blocks.

Items on the deletion list will be deleted fromLearning Media stock and will not be reprinted.

24

THE NUMERACY REFERENCE GROUP:

ACKNOWLEDGMENTSThe Ministry of Education wishes to acknowledge thefollowing people and organisations for their contributiontowards the development of this supplement.

THE PARTICIPANTS:The New Zealand numeracy project personnel �facilitators and principals, teachers, and children frommore than eighteen hundred New Zealand schools whocontributed to this handbook through their participationin the numeracy development projects from 2000�2005.

Professor Derek Holton, convenor (The University ofOtago), Professor Megan Clark (Victoria University ofWellington), Dr Joanna Higgins (Victoria University ofWellington College of Education), Dr Gill Thomas (MathsTechnology Limited), Associate Professor Jenny Young-Loveridge (The University of Waikato), AssociateProfessor Glenda Anthony (Massey University), TonyTrinick (The University of Auckland Faculty ofEducation), Garry Nathan (The University of Auckland),Paul Vincent (Education Review Office), Dr JoannaWood (New Zealand Association of MathematicsTeachers), Peter Hughes (The University of AucklandFaculty of Education), Vince Wright (The University ofWaikato School Support Services), Geoff Woolford(Parallel Services), Kevin Hannah (Christchurch Collegeof Education), Chris Haines (School Trustees�Association), Linda Woon (NZPF), Jo Jenks (VictoriaUniversity of Wellington College of Education, EarlyChildhood Division), Bill Noble (New ZealandAssociation of Intermediate and Middle Schools), DianeLeggatt of Karori Normal School (NZEI Te Riu Roa),Sului Mamea (Pacific Island Advisory Group, PalmerstonNorth), Dr Sally Peters (The University of WaikatoSchool of Education), Pauline McNeill of ColumbaCollege (PPTA), Dr Ian Christensen (He Kupenga Hao ite Reo), Liz Ely (Education Review Office), Ro Parsons(Ministry of Education), Malcolm Hyland (Ministry ofEducation).

THE ORIGINAL WRITERS,REVIEWERS, AND PUBLISHERS:The BSM Review Group: Eleanor Burt (ChristchurchCollege of Education) (Chair), Errolyn Taane (DunedinCollege of Education), Lynn Tozer (Dunedin College ofEducation), Chris Henderson (Christchurch College ofEducation), Margaret Farrelly (Christchurch College ofEducation), Dale Hendry (Wellington College ofEducation), David MacDonald, Kirsty Farquharson,Jocelyn Cranefield, Jan Kokason (Learning MediaLimited), Joe Morrison, Dr Gill Thomas (MathsTechnology Limited).

In addition, the Ministry of Education wishes toacknowledge Professor Bob Wright (Southern CrossUniversity, Lismore, NSW), Dr Noel Thomas (CharlesSturt University, Bathhurst, NSW), Dr KoenoGravemeijer (Freudenthal Institute, Utrecht,Netherlands), Jim Martland (The University ofManchester, UK), and Susan Lamon (MarquetteUniversity, USA).

The Ministry of Education also wishes to acknowledgeThe New South Wales Department of Education andTraining for permission to trial Count Me in Too in 2000through a one-year arrangement. The findings from theuse of this pilot project informed the development of thenumeracy policy in New Zealand.

Count Me In Too is the registered Trade Mark of theCrown in the Right of the State of New South Wales(Department of Education and Training). Copyright ofthe Count Me In Too Professional DevelopmentPackage materials (1997-2002), including the LearningFramework in Number and the Schedule for EarlyNumber Assessment, is also held by the Crown in theRight of the State of New South Wales (Department ofEducation and Training) 2002.

The cover design is by Dave Maunder (Learning MediaLimited) and Base Two Design Ltd.

All illustrations copyright © Crown 2006 except: Digitalimagery of the conch copyright © 2000 PhotoDisc, Inc.